Finite Group Databasebeta

← #13148810

Subgroups — #13148810

Order 1728.

1064 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×D3×D9C211yesmaximal, characteristic, complemented
2C2×#88641C211yesmaximal, characteristic, complemented
3#11721752C211yesmaximal, characteristic, complemented
4C9×#893C211yesmaximal, characteristic, complemented
5C3×#63456C211yesmaximal, characteristic, complemented
6#11721050C211yesmaximal, characteristic, complemented
7#11721049C211yesmaximal, characteristic, complemented
8#11721041C211yesmaximal, characteristic, complemented
9#11721031C211yesmaximal, characteristic, complemented
10#11721030C211yesmaximal, characteristic, complemented
11#11721024C211yesmaximal, characteristic, complemented
12#11721016C211yesmaximal, characteristic, complemented
13#11720977C211yesmaximal, characteristic, complemented
14#11720976C211yesmaximal, characteristic, complemented
15#11720974C211yesmaximal, characteristic, complemented
16#10594614—31nomaximal
17#10589649—31nomaximal
18C22×D3×D9C2211yescharacteristic
19C2×C4×C3⋊D9C2211yescharacteristic
20C2×#6226C2211yescharacteristic, complemented
21C2×C9×D12C2211yescharacteristic
22C2×C4×D3×C9C2211yescharacteristic
23C2×C4×D3×C9C2211yescharacteristic, complemented
24C2×C3×D36C2211yescharacteristic
25C2×C3×C4×D9C2211yescharacteristic
26C2×#6195C2211yescharacteristic
27C2×#6194C2211yescharacteristic
28C2×#6194C2211yescharacteristic
29C2×#6194C2211yescharacteristic, complemented
30C2×D3×Dic9C2211yescharacteristic
31C2×#6192C2211yescharacteristic
32C2×(C3⋊D9)⋊C4C2211yescharacteristic
33C2×Dic3×D9C2211yescharacteristic
34C2×Dic3×D9C2211yescharacteristic, complemented
35C4×D3×D9—24no—
36#88641—24no—
37C3×C9×C4⋊C4C2211yescharacteristic, complemented
38#88536C2211yescharacteristic
39#88536C2211yescharacteristic
40#88534C2211yescharacteristic, complemented
41#88534C2211yescharacteristic, complemented
42C9×(C2×D3)⋊C4C2211yescharacteristic
43C9×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C3×(C2×D9)⋊C4C2211yescharacteristic
45C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
46C3×(C2×D9)⋊C4C2211yescharacteristic, complemented
47C4×C9×Dic3C2211yescharacteristic, complemented
48C3×Dic9⋊C4C2211yescharacteristic, complemented
49(C2×D3)⋊Dic9C2211yescharacteristic
50(C2×D3)⋊Dic9C2211yescharacteristic, complemented
51(C2×D9)⋊Dic3C2211yescharacteristic
52Dic3⋊Dic9C2211yescharacteristic, complemented
53#88442C2211yescharacteristic, complemented
54Dic3×Dic9C2211yescharacteristic, complemented
55C2×C4×D32—31no—
56C2×#3795—31no—
57#64105—31no—
58C3×#894—31no—
59C3×#893D311yescharacteristic
60#63922—31no—
61#63922—31no—
62#63912—31no—
63#63905—31no—
64#63904—31no—
65#63896—31no—
66#63885—31no—
67#63880—31no—
68#63879—31no—
69#63877—31no—
70C2×#3697—31no—
71C22×C4×D9—31no—
72C4×D4×C9—31no—
73#63501—31no—
74#63499—31no—
75C4×#611—31no—
76C4×#611—31no—
77#63458—31no—
78#63458—61no—
79#63456D311yescharacteristic, complemented
80#63446—31no—
81#63445—31no—
82#63444—31no—
83#63440—31no—
84C4×D36—31no—
85#63434—31no—
86C22×C3⋊D9C2311yescharacteristic
87C22×D3×C9C2311yescharacteristic
88C22×D3×C9C2311yescharacteristic
89C22×C3×D9C2311yescharacteristic
90C22×C3×D9C2311yescharacteristic
91C2×D3×D9—22no—
92C2×D3×D9—22no—
93C2×D3×D9—22no—
94C2×C3×C4×C9C2311yescharacteristic
95C2×C3×C4×C9C2311yescharacteristic
96C2×C3×C4×C9C2311yescharacteristic
97C2×C3⋊Dic9C2311yescharacteristic
98C2×C3⋊Dic9C2311yescharacteristic
99C2×C3⋊Dic9C2311yescharacteristic
100C4×C3⋊D9—22no—
101#6226—22no—
102C2×C9×Dic3C2311yescharacteristic
103C2×C9×Dic3C2311yescharacteristic
104C2×C3×Dic9C2311yescharacteristic
105C2×C3×Dic9C2311yescharacteristic
106C9×D12—22no—
107C4×D3×C9—22no—
108C4×D3×C9—22no—
109C3×D36—22no—
110C3×C4×D9—22no—
111#6195—22no—
112#6194—22no—
113#6194—22no—
114#6194—22no—
115D3×Dic9—22no—
116#6192—22no—
117(C3⋊D9)⋊C4—22no—
118Dic3×D9—22no—
119Dic3×D9D414yescomplemented
120#5656—91no—
121#5547—91no—
122C22×D32—31no—
123C2×C4×C3⋊D3—31no—
124C2×#634—31no—
125C2×C3×D12—31no—
126C2×C3×D12C2×D311yescharacteristic
127C2×C3×C4×D3—31no—
128C2×C3×C4×D3C2×D311yescharacteristic
129C2×C3×C4×D3C2×D311yescharacteristic
130C2×#626—31no—
131C2×#626—31no—
132C2×#625—31no—
133C2×#625—31no—
134C2×#625—31no—
135C2×#624—31no—
136C2×D3×Dic3—31no—
137C2×D3×Dic3—31no—
138C2×D3×Dic3—31no—
139C4×D32—64no—
140#3795—64no—
141C23×D9—31no—
142C32×C4⋊C4C2×D311yescharacteristic
143#3752—31no—
144#3752—31no—
145#3750—31no—
146#3750—31no—
147C3×(C2×D3)⋊C4—31no—
148C3×(C2×D3)⋊C4—31no—
149C3×(C2×D3)⋊C4—31no—
150C3×(C2×D3)⋊C4C2×D311yescharacteristic
151C3×(C2×D3)⋊C4C2×D311yescharacteristic
152C3×Dic3⋊C4—31no—
153C3×C4×Dic3C2×D311yescharacteristic
154#3724—31no—
155Dic3⋊Dic3—31no—
156(C2×D3)⋊Dic3—31no—
157(C2×D3)⋊Dic3—31no—
158(C2×D3)⋊Dic3—31no—
159Dic32—31no—
160C2×D4×C9—31no—
161C22×C4×C9—31no—
162C22×C4×C9—31no—
163C2×#611—31no—
164C2×#611—31no—
165C2×#611—31no—
166C2×#611—31no—
167C22×Dic9—31no—
168#3697—64no—
169C2×D36—31no—
170C2×D36C2×D311yescharacteristic
171C2×C4×D9—31no—
172C2×C4×D9—31no—
173C2×C4×D9—31no—
174C2×C4×D9—31no—
175C2×C4×D9—64no—
176C2×C4×D9—61no—
177C2×C4×D9C2×D311yescharacteristic
178C2×Dic18—31no—
179C2×Dic18—61no—
180C9×C4⋊C4—21no—
181C9×C4⋊C4C2×D311yescharacteristic, complemented
182C9×C22⋊C4—31no—
183C9×C22⋊C4—31no—
184C42×C9—31no—
185#3676—31no—
186#3676—31no—
187(C2×D9)⋊C4—31no—
188(C2×D9)⋊C4—31no—
189(C2×D9)⋊C4—31no—
190(C2×D9)⋊C4—61no—
191(C2×D9)⋊C4—61no—
192(C2×D9)⋊C4C2×D311yescharacteristic
193(C2×D9)⋊C4C2×D311yescharacteristic, complemented
194(C2×D9)⋊C4C2×D311yescharacteristic, complemented
195C4⋊Dic9—31no—
196Dic9⋊C4—31no—
197Dic9⋊C4—31no—
198Dic9⋊C4—31no—
199Dic9⋊C4—61no—
200Dic9⋊C4—61no—
201Dic9⋊C4C2×D311yescharacteristic, complemented
202C4×Dic9—31no—
203C22×C3×C9C2411yescharacteristic
204C2×C3⋊D9—21no—
205C2×C3⋊D9—21no—
206C2×C3⋊D9#4112yescomplemented
207C2×D3×C9—21no—
208C2×D3×C9—21no—
209C2×D3×C9—21no—
210C2×D3×C9—21no—
211C2×D3×C9—21no—
212C2×D3×C9#4112yescomplemented
213C2×C3×D9—21no—
214C2×C3×D9—21no—
215C2×C3×D9—21no—
216C2×C3×D9—21no—
217C2×C3×D9—21no—
218C2×C3×D9C2×D412yes—
219D3×D9—28no—
220C3×C4×C9—21no—
221C3×C4×C9—21no—
222C3×C4×C9—21no—
223C3⋊Dic9—21no—
224C3⋊Dic9—21no—
225C3⋊Dic9C2×D412yes—
226C9×Dic3—21no—
227C9×Dic3C2×D412yes—
228C3×Dic9—21no—
229C3×Dic9—21no—
230C2×#237—91no—
231C2×#235—91no—
232C22×C4×D3—91no—
233C22×C4×D3—91no—
234C3×#123—91no—
235C3×C4×D4—31no—
236#939—91no—
237#937—91no—
238#937—91no—
239#929—91no—
240C4×#67—91no—
241C4×#67—91no—
242#896—91no—
243#896—91no—
244#896—91no—
245#896—181no—
246#894—31no—
247#893—91no—
248#893D911yescharacteristic, complemented
249#884—91no—
250#884—91no—
251#884—91no—
252#883—91no—
253#882—91no—
254#882—91no—
255#67⋊C4—91no—
256#67⋊C4—91no—
257#878—91no—
258#877—91no—
259C4×D12—91no—
260#872—91no—
261C22×C3⋊D3—31no—
262C22×C3×D3—31no—
263C22×C3×D3—31no—
264C22×C3×D3C22×D311yescharacteristic
265C22×C3×D3C22×D311yescharacteristic
266C2×D32—62no—
267C2×D32—62no—
268C2×D32—62no—
269C2×C32×C4C22×D311yescharacteristic
270C2×C32×C4C22×D311yescharacteristic
271C2×C32×C4C22×D311yescharacteristic
272C2×C3⋊Dic3—31no—
273C2×C3⋊Dic3—31no—
274C2×C3⋊Dic3—31no—
275C4×C3⋊D3—62no—
276#634—62no—
277C2×C3×Dic3—31no—
278C2×C3×Dic3—31no—
279C2×C3×Dic3C22×D311yescharacteristic
280C2×C3×Dic3C22×D311yescharacteristic
281C3×D12—22no—
282C3×D12—62no—
283C3×C4×D3—22no—
284C3×C4×D3—22no—
285C3×C4×D3—62no—
286#626—62no—
287#626—62no—
288#625—62no—
289#625—62no—
290#625—62no—
291#624—62no—
292D3×Dic3—34no—
293D3×Dic3—62no—
294D3×Dic3—62no—
295C23×C9—31no—
296C23×C9—31no—
297C22×D9—31no—
298C22×D9—61no—
299C22×D9—62no—
300C22×D9—62no—
301C22×D9—62no—
302C22×D9C22×D311yescharacteristic
303C22×D9C22×D311yescharacteristic
304D4×C9—62no—
305C2×C4×C9—21no—
306C2×C4×C9—21no—
307C2×C4×C9—21no—
308C2×C4×C9—31no—
309C2×C4×C9—31no—
310C2×C4×C9—62no—
311C2×C4×C9—62no—
312C2×C4×C9C22×D311yescharacteristic
313C2×C4×C9C22×D311yescharacteristic
314C2×C4×C9C22×D311yescharacteristic
315#611—62no—
316#611—62no—
317#611—62no—
318#611—62no—
319C2×Dic9—31no—
320C2×Dic9—31no—
321C2×Dic9—31no—
322C2×Dic9—61no—
323C2×Dic9—61no—
324C2×Dic9—61no—
325C2×Dic9—62no—
326C2×Dic9C22×D311yescharacteristic
327C2×Dic9C22×D311yescharacteristic
328D36—22no—
329D36—62no—
330C4×D9—22no—
331C4×D9—34no—
332C4×D9—62no—
333C4×D9—62no—
334C4×D9—62no—
335C4×D9—122no—
336Dic18—62no—
337Dic18—122no—
338#525—271noSylow
339C2×C3×C9C22×D411yescharacteristic
340C2×C3×C9C2×#4111yescharacteristic
341C2×C3×C9C2×#4111yescharacteristic
342C3⋊D9—22no—
343D3×C9—22no—
344D3×C9—41no—
345C3×D9—22no—
346C3×D9—41no—
347C23×D3—91no—
348C23×D3—91no—
349C2×C3×D4—31no—
350C2×C3×D4—91no—
351C22×C3×C4—31no—
352C22×C3×C4—31no—
353C22×C3×C4—91no—
354C2×#67—91no—
355C2×#67—91no—
356C2×#67—91no—
357C2×#67—91no—
358C2×#67—91no—
359C2×#67—91no—
360C2×#67—91no—
361C2×#67—91no—
362C22×Dic3—91no—
363C22×Dic3—91no—
364C22×Dic3—91no—
365#237—184no—
366#235—184no—
367C2×D12—31no—
368C2×D12—91no—
369C2×D12—91no—
370C2×D12C2×D911yescharacteristic
371C2×C4×D3—31no—
372C2×C4×D3—91no—
373C2×C4×D3—91no—
374C2×C4×D3—91no—
375C2×C4×D3—91no—
376C2×C4×D3—91no—
377C2×C4×D3—91no—
378C2×C4×D3—91no—
379C2×C4×D3—181no—
380C2×C4×D3—184no—
381C2×C4×D3—184no—
382C2×C4×D3C2×D911yescharacteristic
383C2×C4×D3C2×D911yescharacteristic, complemented
384C2×Dic6—91no—
385C2×Dic6—91no—
386C2×Dic6—181no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4—91no—
389C3×C4⋊C4C2×D911yescharacteristic, complemented
390C3×C4⋊C4D3211yescharacteristic
391C3×C22⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—91no—
394C3×C22⋊C4—91no—
395C3×C22⋊C4—91no—
396C3×C42—31no—
397#217—91no—
398#217—91no—
399#217—91no—
400(C2×D3)⋊C4—31no—
401(C2×D3)⋊C4—31no—
402(C2×D3)⋊C4—31no—
403(C2×D3)⋊C4—91no—
404(C2×D3)⋊C4—91no—
405(C2×D3)⋊C4—91no—
406(C2×D3)⋊C4—91no—
407(C2×D3)⋊C4—91no—
408(C2×D3)⋊C4—91no—
409(C2×D3)⋊C4—91no—
410(C2×D3)⋊C4—181no—
411(C2×D3)⋊C4—181no—
412(C2×D3)⋊C4C2×D911yescharacteristic
413(C2×D3)⋊C4C2×D911yescharacteristic, complemented
414C4⋊Dic3—91no—
415Dic3⋊C4—31no—
416Dic3⋊C4—91no—
417Dic3⋊C4—91no—
418Dic3⋊C4—91no—
419Dic3⋊C4—91no—
420Dic3⋊C4—91no—
421Dic3⋊C4—91no—
422Dic3⋊C4—91no—
423Dic3⋊C4—181no—
424Dic3⋊C4—181no—
425C4×Dic3—91no—
426C4×Dic3—91no—
427C4×Dic3C2×D911yescharacteristic, complemented
428C22×C32C23×D311yescharacteristic
429C2×C3⋊D3—32no—
430C2×C3⋊D3—61no—
431C2×C3⋊D3—61no—
432C2×C3×D3—21no—
433C2×C3×D3—21no—
434C2×C3×D3—21no—
435C2×C3×D3—21no—
436C2×C3×D3—21no—
437C2×C3×D3—32no—
438C2×C3×D3—61no—
439C2×C3×D3—61no—
440C2×C3×D3—61no—
441C2×C3×D3—61no—
442C2×C3×D3—61no—
443C2×C3×D3#23512yes—
444D32—68no—
445C32×C4—21no—
446C32×C4—21no—
447C32×C4—21no—
448C3⋊Dic3—32no—
449C3⋊Dic3—61no—
450C3⋊Dic3—61no—
451C3×Dic3—21no—
452C3×Dic3—61no—
453C3×Dic3—61no—
454C3×Dic3D3×D412yes—
455C22×C9—21no—
456C22×C9—32no—
457C22×C9—61no—
458C22×C9—61no—
459C22×C9—61no—
460C22×C9—61no—
461C22×C9—61no—
462C22×C9C23×D311yescharacteristic
463C2×D9—21no—
464C2×D9—21no—
465C2×D9—21no—
466C2×D9—21no—
467C2×D9—21no—
468C2×D9—32no—
469C2×D9—62no—
470C2×D9—68no—
471C2×D9—61no—
472C2×D9—61no—
473C2×D9—121no—
474C2×D9—121no—
475C2×D9D3×D412yes—
476C4×C9—21no—
477C4×C9—21no—
478C4×C9—21no—
479C4×C9—32no—
480C4×C9—41no—
481C4×C9—41no—
482C4×C9—41no—
483C4×C9—61no—
484Dic9—21no—
485Dic9—21no—
486Dic9—32no—
487Dic9—62no—
488Dic9—61no—
489Dic9—61no—
490Dic9—121no—
491Dic9—121no—
492C2×#41—271no—
493C23×C4—271no—
494#123—91no—
495#123—271no—
496C22⋊Q8—271no—
497C22⋊Q8—271no—
498#121—271no—
499#121—271no—
500#120—271no—
501#120—271no—
502C4×D4—31no—
503C4×D4—271no—
504C4×D4—271no—
505C4×D4—271no—
506#117—271no—
507C3×C9#52511yescharacteristic, complemented, Sylow
508C23×C3—31no—
509C23×C3—31no—
510C23×C3—91no—
511C23×C3—91no—
512C22×D3—31no—
513C22×D3—31no—
514C22×D3—91no—
515C22×D3—91no—
516C22×D3—181no—
517C22×D3—182no—
518C22×D3—182no—
519C22×D3—182no—
520C22×D3—182no—
521C22×D3—182no—
522C22×D3—182no—
523C22×D3C22×D911yescharacteristic
524C22×D3C22×D911yescharacteristic
525C3×D4—62no—
526C3×D4—182no—
527C2×C3×C4—21no—
528C2×C3×C4—21no—
529C2×C3×C4—21no—
530C2×C3×C4—31no—
531C2×C3×C4—31no—
532C2×C3×C4—62no—
533C2×C3×C4—62no—
534C2×C3×C4—91no—
535C2×C3×C4—91no—
536C2×C3×C4—182no—
537C2×C3×C4C22×D911yescharacteristic
538C2×C3×C4C22×D911yescharacteristic
539C2×C3×C4C22×D911yescharacteristic
540C2×C3×C4C2×D3211yescharacteristic
541C2×C3×C4C2×D3211yescharacteristic
542C2×C3×C4C2×D3211yescharacteristic
543#67—182no—
544#67—182no—
545#67—182no—
546#67—182no—
547#67—182no—
548#67—182no—
549#67—182no—
550#67—182no—
551C2×Dic3—31no—
552C2×Dic3—31no—
553C2×Dic3—91no—
554C2×Dic3—91no—
555C2×Dic3—94no—
556C2×Dic3—91no—
557C2×Dic3—91no—
558C2×Dic3—91no—
559C2×Dic3—91no—
560C2×Dic3—181no—
561C2×Dic3—181no—
562C2×Dic3—181no—
563C2×Dic3—182no—
564C2×Dic3—182no—
565C2×Dic3C22×D911yescharacteristic
566C2×Dic3C22×D911yescharacteristic
567D12—22no—
568D12—62no—
569D12—182no—
570D12—182no—
571C4×D3—22no—
572C4×D3—22no—
573C4×D3—62no—
574C4×D3—94no—
575C4×D3—182no—
576C4×D3—182no—
577C4×D3—182no—
578C4×D3—182no—
579C4×D3—182no—
580C4×D3—182no—
581C4×D3—362no—
582Dic6—182no—
583Dic6—182no—
584Dic6—362no—
585C2×C32C2×#23511yescharacteristic
586C2×C32C2×D3×D411yescharacteristic
587C2×C32D3×#4111yescharacteristic
588C3⋊D3—62no—
589C3×D3—22no—
590C3×D3—41no—
591C3×D3—62no—
592C3×D3—121no—
593C2×C9—21no—
594C2×C9—21no—
595C2×C9—21no—
596C2×C9—62no—
597C2×C9—121no—
598C2×C9C2×D3×D411yescharacteristic
599C2×C9D3×#4111yescharacteristic
600C2×C9D3×#4111yescharacteristic
601D9—22no—
602D9—41no—
603D9—62no—
604D9—122no—
605C24—271no—
606#41—544no—
607C2×Q8—271no—
608C2×D4—31no—
609C2×D4—91no—
610C2×D4—271no—
611C2×D4—271no—
612C2×D4—271no—
613C2×D4—271no—
614C2×D4—271no—
615C22×C4—31no—
616C22×C4—31no—
617C22×C4—91no—
618C22×C4—271no—
619C22×C4—271no—
620C22×C4—271no—
621C22×C4—271no—
622C22×C4—271no—
623C22×C4—544no—
624C4⋊C4—91no—
625C4⋊C4—271no—
626C4⋊C4—271no—
627C4⋊C4—271no—
628C4⋊C4—271no—
629C4⋊C4D3×D911yescharacteristic, complemented
630C22⋊C4—31no—
631C22⋊C4—31no—
632C22⋊C4—91no—
633C22⋊C4—91no—
634C22⋊C4—91no—
635C22⋊C4—271no—
636C22⋊C4—271no—
637C22⋊C4—271no—
638C22⋊C4—271no—
639C22⋊C4—271no—
640C42—31no—
641C42—271no—
642C22×C3—21no—
643C22×C3—32no—
644C22×C3—61no—
645C22×C3—61no—
646C22×C3—61no—
647C22×C3—61no—
648C22×C3—61no—
649C22×C3—92no—
650C22×C3—181no—
651C22×C3—181no—
652C22×C3—181no—
653C22×C3—181no—
654C22×C3—181no—
655C22×C3C23×D911yescharacteristic
656C22×C3C22×D3211yescharacteristic
657C2×D3—21no—
658C2×D3—21no—
659C2×D3—21no—
660C2×D3—21no—
661C2×D3—21no—
662C2×D3—32no—
663C2×D3—61no—
664C2×D3—61no—
665C2×D3—61no—
666C2×D3—61no—
667C2×D3—61no—
668C2×D3—92no—
669C2×D3—92no—
670C2×D3—182no—
671C2×D3—188no—
672C2×D3—188no—
673C2×D3—181no—
674C2×D3—181no—
675C2×D3—181no—
676C2×D3—181no—
677C2×D3—361no—
678C2×D3—361no—
679C2×D3#369712yescomplemented
680C3×C4—21no—
681C3×C4—21no—
682C3×C4—21no—
683C3×C4—21no—
684C3×C4—21no—
685C3×C4—21no—
686C3×C4—32no—
687C3×C4—41no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—61no—
691C3×C4—181no—
692C3×C4—181no—
693Dic3—21no—
694Dic3—61no—
695Dic3—61no—
696Dic3—92no—
697Dic3—92no—
698Dic3—182no—
699Dic3—181no—
700Dic3—181no—
701Dic3—181no—
702Dic3—181no—
703Dic3—361no—
704Dic3—361no—
705Dic3D4×D912yes—
706C32#554711yescharacteristic
707C9—21no—
708C9#565611yescharacteristic, complemented
709C23—31no—
710C23—31no—
711C23—91no—
712C23—91no—
713C23—271no—
714C23—542no—
715C23—542no—
716C23—542no—
717Q8—542no—
718D4—62no—
719D4—182no—
720D4—542no—
721D4—542no—
722D4—542no—
723D4—542no—
724D4—542no—
725C2×C4—31no—
726C2×C4—31no—
727C2×C4—62no—
728C2×C4—62no—
729C2×C4—91no—
730C2×C4—91no—
731C2×C4—182no—
732C2×C4—274no—
733C2×C4—271no—
734C2×C4—271no—
735C2×C4—271no—
736C2×C4—542no—
737C2×C4—542no—
738C2×C4—542no—
739C2×C4—542no—
740C2×C4C2×D3×D911yescharacteristic
741C2×C4C2×D3×D911yescharacteristic
742C2×C4C2×D3×D911yescharacteristic
743C2×C3—21no—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—62no—
747C2×C3—121no—
748C2×C3—182no—
749C2×C3—361no—
750C2×C3C2×#369711yescharacteristic
751C2×C3C2×D4×D911yescharacteristic
752C2×C3#41×D911yescharacteristic
753C2×C3D3×#23511yescharacteristic
754C2×C3D32×D411yescharacteristic
755C2×C3#6431911yescharacteristic
756D3—22no—
757D3—41no—
758D3—62no—
759D3—121no—
760D3—182no—
761D3—182no—
762D3—362no—
763C22—32no—
764C22—61no—
765C22—61no—
766C22—61no—
767C22—61no—
768C22—61no—
769C22—92no—
770C22—181no—
771C22—181no—
772C22—181no—
773C22—181no—
774C22—181no—
775C22—272no—
776C22—548no—
777C22—541no—
778C22—541no—
779C22C22×D3×D911yescharacteristic
780C4—21no—
781C4—21no—
782C4—21no—
783C4—32no—
784C4—61no—
785C4—181no—
786C4—181no—
787C4—272no—
788C4—541no—
789C4—541no—
790C3—21no—
791C3#1058964911yescharacteristic, complemented
792C3#1059461411yescharacteristic
793C2—62no—
794C2—121no—
795C2—182no—
796C2—361no—
797C2—542no—
798C2D3×#369711yescharacteristic
799C2D3×D4×D911yescharacteristic
800C2#1172251411yescharacteristic
subgroupG/H
centerC22C22×D3×D9
commutator, cosocleC22×C3×C9C24
FrattiniC22×C3C22×D32
FittingC3×C9×C4⋊C4C22
socleC22×C32C23×D3
hypercenterC4⋊C4D3×D9
hypocenterC3×C9#525
LCSG ▷ C22×C3×C9 ▷ C3×C9
UCSC1 ◁ C22 ◁ C4⋊C4

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×C4×D3×D9C2semidirect
2. C2×#88641C2semidirect
3. #11721752C2semidirect
4. C9×#893C2semidirect
5. C3×#63456C2semidirect
6. #11721050C2semidirect
7. #11721049C2semidirect
8. #11721041C2semidirect
9. #11721031C2semidirect
10. #11721030C2semidirect
11. #11721024C2semidirect
12. #11721016C2semidirect
13. #11720977C2semidirect
14. #11720976C2semidirect
15. #11720974C2semidirect
20. C2×#6226C22semidirect
23. C2×C4×D3×C9C22semidirect
29. C2×#6194C22semidirect
34. C2×Dic3×D9C22semidirect
37. C3×C9×C4⋊C4C22semidirect
40. #88534C22semidirect
41. #88534C22semidirect
43. C9×(C2×D3)⋊C4C22semidirect
45. C3×(C2×D9)⋊C4C22semidirect
46. C3×(C2×D9)⋊C4C22semidirect
47. C4×C9×Dic3C22semidirect
48. C3×Dic9⋊C4C22semidirect
50. (C2×D3)⋊Dic9C22semidirect
52. Dic3⋊Dic9C22semidirect
53. #88442C22semidirect
54. Dic3×Dic9C22semidirect
79. #63456D3semidirect
119. Dic3×D9D4semidirect
181. C9×C4⋊C4C2×D3semidirect
193. (C2×D9)⋊C4C2×D3semidirect
194. (C2×D9)⋊C4C2×D3semidirect
201. Dic9⋊C4C2×D3semidirect
206. C2×C3⋊D9#41semidirect
212. C2×D3×C9#41semidirect
248. #893D9semidirect
383. C2×C4×D3C2×D9semidirect
389. C3×C4⋊C4C2×D9semidirect
413. (C2×D3)⋊C4C2×D9semidirect
427. C4×Dic3C2×D9semidirect
507. C3×C9#525semidirect
629. C4⋊C4D3×D9semidirect
679. C2×D3#3697semidirect
708. C9#5656semidirect
791. C3#10589649semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×C4×D3×D92
C2×#886412
#117217522
C9×#8932
C3×#634562
#117210502
#117210492
#117210412
#117210312
#117210302
#117210242
#117210162
#117209772
#117209762
#117209742
#105946143
#105896493